Method and apparatus for the analysis of seismic records



March 22, 1966 w, COX 3,242,326

METHOD AND APPARATUS FOR THE ANALYSIS OF SEISMIC RECORDS Original FiledOct. 26, 1954 4 Sheets-Sheet l I ,A A W I W A A 5 W MM H l I ('7') MTT--- FIG. I.

INVENTOR.

WILLIAM H. COX

ATTORNEYS March 22, 1966 w. H. cox 3,242,326

METHOD AND APPARATUS FOR THE ANALYSIS OF SEISMIC RECORDS Original FiledOct. 26, 1954 4 Sheets-Sheet 2 March 22, 1966 w, cox 3,242,326

METHOD AND APPARATUS FOR THE ANALYSIS OF SEISMIC RECORDS Original FiledOct. 26, 1954 4 Sheets-Sheet 5 ATTORNEYS March 22, 1966 w cox 3,242,326

METHOD AND APPARATUS FOR THE ANALYSIS OF SEISMIC RECORDS Original FiledOct. 26, 1954 4 Sheets-Sheet L INVENTOR.

WILLIAM H. COX BY /2/--Q -1 L l zl 1 /ZL v\- ATTORNEY United StatesPatent 3,242,326 METHOD AND APPARATUS FOR THE ANALYEIS 0F SEISMICRECORDS William H. Cox, Beaumont, Tex., assignor to Sun Oil Company,Philadelphia, Pa., a corporation of New Jersey Continuation ofapplication Ser. No. 464,843, Oct. 26, 1954. This application June 29,1959, Ser. No. 823,772 5 Claims. (Cl. 235-481) This invention relates tomethods and apparatus for the analysis of seismic records and hasparticular reference to the accentuation of reflections againstbackground noise.

This application is a continuation of my application, Serial No.464,843, filed October 26, 1954, now abandoned.

A major problem in seismic reflection geophysical exploration is that ofrecognition of reflection records against background noise. Filters are,accordingly, used since experience has shown that certain frequencybands are primarily involved in the desired signals and, consequently,by filtering the detected signals there is achieved some segregation ofthe desired signals from those which have frequencies outside the passbands of the filters and are of no interest. Design of a conventionalfilter, however, necessarily involves a compromise since the desiredsignals actually contain a very broad band of frequencies and removal ofany frequency components will also remove some components of the desiredsignal. In any event, filtering causes a substantial change in thewaveform of the desired signals and reflections cannot be so readilyrecognized by those having experience in this art, since recognition isto a considerable extent by virtue of waveform. Furthermore, it isdiflicult to design a simple filter with the required amplitude versusfrequency response which also has linear phase shift with frequency orzero delay distortion.

Recognition must also be given, in the design of filters, to the factthat the reflections which it is desired to detect are essentiallytransients. A filter which may appear satisfactory on a basis offrequency response and phase shift may be unsatisfactory due to poortransient properties. A poorly designed filter will produce essentiallythe same characteristic damped wave train output for any transientimpulse applied to it. This ringing effect due to stored energy inreactive elements is present to some extent in any conventional filter.

Transient waveform distortion and phase or delay distortion are of majorimportance in recording apparatus used in geophysical exploration. Thesefactors affect accuracy in measurement of the time of occurrence ofseismic reflections. The need for a filter which will remove unwantedfrequencies without producing time error will be apparent.

In accordance with the present invention there is provided a method oftransient waveform analysis in which desired signals are separated fromnoise on the basis of wave shape or character instead of frequencycontent only. The nature of the invention may be briefly stated asfollows:

On theoretical bases, there has been computed the waveform which shouldappear at a detector as the result of reflection in the earth of a pulseresulting from a shot. This computation of a wave shape is, of course,based on theoretical assumptions, but it does appear that what actuallyoccurs in practice conforms reasonably with the theoretical.

In accordance with the present invention a record made by a seismographis scanned against such a theoretical type of waveform, in the sensethat the product of the amplitude of such waveform with a portion of theseismic record is integrated over a suitable interval to give rise to aderived record in which the reflections are accentuated. In effect, afiltering action is thus achieved with suppression of the components ofthe original record which are not of significance.

The foregoing will be made clearer in the following description read inconjunction with the accompanying drawings, in which:

FIGURE 1 is a diagram illustrative of the method herein involved, FIGURE1 also including a pair of formulae pertaining thereto;

FIGURE 2 is a diagram showing a preferred form of apparatus used forcarrying out the improved method;

FIGURE 3 is a diagram showing an alternative form of apparatus forcarrying out the method; and

FIGURE 4 is a diagram showing apparatus for carrying out the method inan optical fashion.

The theoretical aspects of the invention may be best described withreference to FIGURE 1.

In this figure there is indicated at I a portion of a seismic recordwhich is typical of that ordinarily secured at a detector. It may beassumed that this record indicates a reflection at R, but as will beevident this reflection is submerged in waves which would ordinarilymake it difficult of recognition except by close comparison withcompanion records made by other seismographs in the same spread. Therecord may be considered as a function of time as indicated, theprogression of time being indicated by the arrow designated 1.

There is indicated at H a waveform which will for convenience behereafter referred to as a wavelet. As shown, this wavelet has a formsuch as has been theoretically deduced to be that which would beproduced by the signal from a shot reflected back to the surface from asubterranean reflecting boundary. A discussion of this type of waveletwill be found, for example, in the article The Form and Nature ofSeismic Waves and the Structure of Seismograms by Norman Ricker, inGeophysics, 1940, page 348, volume 5. It will, of course, be understoodthat this wavelet is theoretical only, and tests and experiments mayindicate that for certain generally known conditions encountered inpractice the wavelet resulting from a reflected pulse may havesubstantially different shape. As will appear, the invention is notlimited to the use of a particular shape of wavelet, but may involve theuse of such wavelets as experience may show are more representative ofthe results of reflection with background noises eliminated. Generally,however, it can be expected that a wavelet thus produced would have arelatively short duration, involving only a limited number of positiveand negative excursions with substantially zero values prior to andsubsequent to a short interval. For present purposes it may be assumedthat the wavelet has an essentially zero value prior to the timeindicated at T and subsequent to the time indicated at T. As shown, itis symmetrical about the central time indicated at zero for the timescale, which zero of time may be considered to be the time t of the waveat I. In accordance with the present invention, the wavelet shown in IImay be considered as progressed in the direction of increasing timealong the seismic record I. At each instant the integration of a productmay be considered to take place as follows:

For each value of the wavelet, it may be considered that that value ismultiplied by the amplitude of the seismic record at corresponding time,and that these products are integrated between the limits T and T, andthe value of the integral is ascribed to a time t corresponding to thezero position in the wavelet. The resulting integral, as a function oft, is indicated in curve IH, and the value of this integral as afunction of t is expressed in the formula (1). The object of the presentinvention is broadly that of evaluation of the integral functionexpressed in (1) either accurately or sufficiently approximately for allpractical purposes.

In the preferred form of the invention, the integral is approximated bya summation of the type indicated at (2). In other words, as is usual inmathematics for the approximation of a continuous integral,corresponding discrete values, individually indicated by the subscriptk, of the two functions of I and II are multiplied together, and the sumof the individual products is taken, there being assumed to be it ofthese products. The resulting summation, divided by n, then approximatesthe desired integral with a constant of proportionality. This summationprocedure is indicated at (2).

It will be understood that hereafter when an integral is referred tothere is intended to be indicated not only the true integral given inexpression (1) but also the summation approximation given in (2), itbeing understood that a sufficient value of n is used to secure theapproximation practically necessary for satisfactory results.

Curve III indicates the integral such as will result from themathematical process just outlined, there being indicated at R anaccentuated wave corresponding in its time t to the reflection R of theoriginal seismic record. In general, this resulting reflection record Rwill be selectively accentuated with respect to the remaining portionsof the curve III which may, in the figure, be considered as resultingfrom the integration of the wavelet with respect to the background noiseof the original record.

The action thus resulting may be conveniently referred to as filteringwith the understanding, however, that as that term is used herein withrespect to the invention there is difference over conventionalfiltering, the filtering occurring in the case of the present inventionbeing with respect to waveform rather than merely with respect tocomponent frequencies. Being with respect to waveform, the filter actionis well adapted to short duration non-recurrent signals. The analogy tofiltering, however, will be apparent if there is considered, merely forpurposes of understanding, the procedure involved in expression (1)applied to a continuous sine wave in a curve corresponding to I and asingle cycle of a cosine wave as a Wavelet utilized at II. It will befound that the response corresponding to Ill would then be a sine Wavehaving the same phase as that of the original continuous sine wave. Suchan integration would, of course, correspond to that normally involved inthe ascertaining of the coefficients of a Fourier series, the integralbeing zero for all harmonics occurring in the original wave of thefrequency involved in the sinusoidal wavelet. For frequencies other thanharmonic frequencies there would, of course, be responses, but these arein general suppressed as compared with the value of the integral forcorresponding or nearly corresponding frequencies of the wavelet and theoriginal wave. It will be evident from the discussion just presentedthat the filtering action is essentially different from that provided byconventional wave filters having band pass characteristics. However,with respect to desired components, there is an action which mayproperly be considered that of filtering.

FIGURE 2 shows a practical form of apparatus for carrying out themathematical operations just described, this apparatus providing anapproximation of the integral by summation, and being particularlyadapted to magnetic recording.

In one highly desirable procedure in seismic prospecting, the outputs ofthe seismic detectors of an array are recorded side by side on amagnetic tape providing, usually, an individual recording channel foreach detector, though, as will be presently mentioned, the recording mayoccur on a single tape channel. When channels individual to thedetectors are provided, the seismic signal from each detector is fed toa modulator wherein it is caused to modulate a carrier having afrequency which is high relative to any frequencies occurring in theseismic signals. The purpose of this, aside from making betterrecordings, is to provide a record which may be subjected to successivereproductions for handling during analysis procedures. If a seismicsignal is directly recorded at its own frequencies on a tape, thereproduction of that recording will not be of the original signal butwill rather be of its first time derivative. If this signal, in turn, isrecorded directly, its reproduction will involve the taking of anotherderivative, and so on. In the usual sound recording processes whichutilize magnetic tapes, these successive differentiating steps are notof significance; but in the case of seismic recording the result issuccessive phase shiftings which are detrimental to the ascertainment oftimes of occurrence of particular events on the records afterreproduction. However, if the seismic signals modulate a high frequencycarrier, the time derivatives which occur are only those of the recordedmodulated wave and the phase of the seismic envelope is essentiallyunchanged, whether the modulation is of amplitude or frequency type. Theapparatus described, therefore, will assume that the original magneticrecord is of a modulated carrier.

Recording to the outputs of a plurality of detectors on a singlemagnetic tape channel may be effected by modulation of individualcarriers of different frequencies, the modulated carriers then beingadded together and recorded. Reproduction in such case involvesseparation of the modulated carriers by suitable filters followed bydemodulation to recover the seismic signals.

There is indicated at 2 a magnetic tape which may be assumed to haveeither a plurality of channels or a single channel carrying themodulated carriers resulting from one of the recording procedures justindicated. A channel 4 is indicated thereon with which is associated apick-up head 6, it being understood that if there was multiple channelrecording there may be duplications of the pick-up and the connectedapparatus, one for each channel, or if a number of signals are recordedon a single channel that a single pick-up would be used and interposedbetween it and the next apparatus there would be filtering to segregatea single channel. The output from the pick-up 6 is fed (either with orwithout filtering, as would be suitable for a particular case) to ademodulator and amplifier 8 of conventional type resulting in theproduction of an output at terminals 10 of the original seismic signal.The terminals 10 provide an input of this seismic signal to apparatusindicated generally at 12 which effects integration, by summation, inaccordance with the invention. The apparatus 12 comprises a delay linegenerally indicated at 14 which is shown as comprising a ground line 15and a series of delay elements 16 which may be of any conventional typeto provide between them successive delays of the input from terminals10. The delay line terminates in an impedance at 18 which has thecharacteristic impedance of the delay line to avoid reflection ofsignals traveling therethrough. The junctions of the sections 16 of thedelay line are tapped by the connections 20 which lead to isolatingdevices 22 which in some instances may be relatively high resistancesbut which are, more desirably, isolating elements such as cathodefollowers which will receive and transmit the signals from the junctionswithout affecting the accurate delaying functions of the line. Ifdesired, the elements 22 may also involve voltage amplification.

The outputs from the individual elements 22 are fed to attenuators 24the adjustable contacts 26 of which are either connected through addingresistors 28 to a positive line 30 or through adding resistors 32 to anegative line 34. These lines 30 and 34 are connected to the oppositeterminals of the primary of a transformer 36 the center tap of which isconnected to the ground line through line 38. The output from thesecondary of the transformer 36 is fed to terminals 40 which areconnected to the input of a modulator 42 wherein the signals atterminals 40 are caused to modulate a high frequency carrier to providea modulated carrier to recorder 44 which may record the resultingmodulated signal on another magnetic tape. In the event that it isdesired at this stage to provide a photographic record for examination,the modulator 42 may be omitted, and the output signals from terminals40 may be directly recorded in an oscillograph.

Instead of an electrical delay line such as is indicated at 14 there maybe provided a delay line of mechanical or acoustic type, tappedatintervals by connections corresponding to 20.

Assuming that the delays of the individual sections 16 are equal, thetapped connections 20 and the attenuators 24 Will have the number Itrequired for summation. The wavelet involved in the integration is setinto the attenuators 24 by suitable placement of their adjustablecontacts 26, each providing a voltage division corresponding to theordinate of the wavelet II at a corresponding point of sampling. Thepositive ordinates are set by such adjustment and connection to thepositive line 30, while the negative ordinates are similarly set but byconnection to the negative line 34. As will be evident, at any instantof time, say that indicated at t in FIGURE 1, there will be fed from thetaps between the delay line sections values of the input signalcorresponding to the time increments defined by k in FIGURE 1. Theresult will be that from each attenuator there will be provided anoutput of the product of the corresponding ordinates of the curves I andII. These are then added, with suitable account being taken of signthrough the resistors 28 and 32 with the result that the integralsummation is provided at terminals 40 corresponding to the curve III inFIG- URE 1. The resulting record, therefore, is that produced by thefiltering action in accordance with the present invention, thereflections being accentuated as at R if a suitable choice of wavelethas been made for the conditions involved.

By duplications of the apparatus described, or by repeated recording indifferent channels of the final tape, there will be produced recordscorresponding to the original seismic records of a detector array buthaving been subjected to the filtering action in accordance with theinvention. These records may then be either reproduced for visualinspection photographically or may be subjected to various manipulationsinvolving further filtering, time delays, time rearrangements forstep-outs, weathering corrections, etc., as, for example, described indetail in the patent of Bazzoni, Ellis and Winterhalter No. 2,940,536.

Reference may now be made to FIGURE 3 which shows another form ofapparatus suitable for securing the same results.

In accordance with this figure, the signal of a single seismic channelin the form of a signal at seismic frequencies or a modulated carrierfrom an original tape such as 2 of FIGURE 2 is fed to the input terminal46 which is connected to a series of combination erasing and recordingheads 48 arranged to record on side by side channels on a magnetic tape50 which is driven continuously in the direction of the arrow. Thisdrive should be at a constant predetermined speed. A series of pickups52 is provided, one pick-up for each channel, the pick-ups beingarranged in staggered relationship so as to provide dilferent timedelays between the instants of recording and of pick-up on the tape 50.The outputs from these heads 52 are delivered through connections 54which correspond to the connections 20 in FIGURE 2 (and would containindividual demodulators if the input at 46 consisted of a modulatedcarrier) and, in fact, from this point on in the apparatus it may beidentical with what has been described in FIGURE 2, the connections 54being to the attenuators 56 into which the wavelet is entered byadjustment of their contacts, the outputs from the attenuators beingadded in resistors 58 and 60 corresponding to resistors 28 and 32 andbeing fed to the transformer 62 which provides an output to terminals 64which may be connected through a modulator to a magnetic recorder or,alternatively, directly to a photographic oscillograph. It will beevident that the general operation of the apparatus disclosed in FIG-URE 3 is the same as that disclosed in FIGURE 2, time delays beingprovided, however, through the mechanical delay involved by reason ofthe motion of tape 50 and the placement of the pick-ups 52. It will beevident that the recording heads 48 may be located diagonally across thetape With the pick-up heads 52 directly across the same, if desired.

It should be noted that if modulated carrier signals are not involved,for example on the tape 2 or 50, the signals being instead at seismicfrequencies, and the picked up signals are, therefore, time derivatives,the procedures involved are nevertheless applicable, the wavelet againstwhich integration is effected being then chosen to correspond, e.g.being the time derivative of the wavelet shown in II. The reflectionswill be correspondingly accentuated.

The foregoing devices approximate the integral given in (1) in FIGURE 1by summation of the type indicated at (2). With the value of nsufficiently high, the integral may be approximated to any desireddegree of accuracy. However, the true continuous value of the integralmay be secured in various fashions, not only by multiplication andintegration electronically, but by various optical systems as, forexample, illustrated in FIGURE 4.

In accordance with this figure, a push-pull seismic record 68 isprovided photographically on a motion picture film 66 using conventionalrecording methods. A lamp 70 through a condenser 72 providesillumination of a portion of the film as it advances, and an image ofthe record on the film is projected by means of a lens system 74 on amask which comprises at 76 and 78 push-pull variable densityrepresentation of the wavelet involved in the product and integration.The illumination passing the mask is picked up by a photocell 80 whichis conventionally illustrated in circuit with a battery 82 andtransformer 84 to provide an output to the terminals 86 which may beconnected to a recorder, either magnetic or photographic, in which therecord medium is advanced in synchronism with the film 66. It will beevident that the light reaching the photocell 80 will, at any instant,be proportional to the integral of the product of the correspondingportions of the record 68 and the mask 76, 78, with the result that theoutput is proportional to the integral given at (l) in FIGURE 1.Continuous integration is thus secured. It will be evident that numerousother optical systems may be used for recording, involving variablewidth or variable density recordings, or there may be utilized similarlyphosphorescent images provided on a tape and involving temporary recordsof the seismic signals. Various optical masking means may also be usedto provide the product of the seismic record and the wavelet requiredfor the integration.

In general, push-pull modulation must be used in optical systems to makepossible recording of positive and negative signal variations withcancellation of the steady component. Inclusion of steady (carrier)components in either the recorded signal or in the analyzing opticalmask would produce undesired integral components in the output.

It may be noted that without electrical means the arrangement in FIGURE4 may provide a variable density record of the integral by providingbeyond the mask 76, 7 8 a cylindrical lens which will converge theillumination passing through the mask to a single transverse line pastwhich a photographic film may move in synchronism with l the film 66.From such a variable density record any desired final record may then beproduced in conventional fashion.

It will be clear from the above that numerous types of apparatus may beprovided for the securing of the integration discussed.

It will be evident, furthermore, that the invention is not limited tothe analysis of seismic records, but may be applied in other fieldswhere it is desired to provide filtering of the type herein described byproviding an integral of a product of a waveform and a predeterminedwavelet. In particular, the invention is applicable to the picking outof transients from a continuous waveform when such transients aresubstantially submerged in irrelevant signals or noise. In any suchcase, the particular wavelet chosen for the analysis should be thatsuitable for the purpose and recognized either as that theoretically tobe secured or derived from practical work. The incoming signal to besubjected to analysis, furthermore, need not necessarily be derived froma recording but may have its origin in some operating or detectingapparatus.

In accordance with the above, therefore, it is to be understood that theinvention is of broad scope and not to be considered limited except asrequired by the following claims.

What is claimed is:

1. The new use, for analysis of a seismic waveform varying with time, ofan apparatus which provides at any instant an output comprising productsof corresponding values of a waveform and of a predetermined wavelet,means summing said products over a predetermined time period of theWaveform, said summation being continuously carried out to provide acontinuous integral output, and means recording said integral output asa function of the time scale of said waveform, said new use involvingintroducing a seismic waveform to the apparatus as the waveform involvedand adjusting the apparatus to provide as the wavelet one having theform of an expected reflection of a seismic Wave.

2. The new use, for analysis of a seismic waveform varying with time, ofan apparatus which provides simultaneously a plurality of outputs eachof which represents the value of a Waveform at a predetermined differentinstant of time, means receiving said outputs and multiplying each by apredetermined individual constant proportional to the amplitude of acorresponding instantaneous portion of a wavelet to provide productoutputs, means receiving said product outputs and summing them toprovide a summed output, and means for recording said summed output as afunction of the time scale of said Waveform, said new use involvingintroducing a seismic waveform to the apparatus as the waveform involvedand adjusting the apparatus to provide as the wavelet one having theform of an expected reflection of a seismic wave.

3. The new use, for analysis of a seismic waveform varying with time, ofan apparatus which provides simultaneously a plurality of outputs eachof which represents the value of a waveform at a predetermined differentinstant of time, means comprising a plurality of attenuators individualto said outputs receiving said outputs and multiplying each by apredetermined individual constant, thereby to provide product outputs,means receiving said product outputs and summing them to provide asummed output, and means for recording said summed output as a functionof the time scale of said waveform, said new use involving introducing aseismic waveform to the apparatus as the waveform involved and adjustingsaid attenuators so that each individual constant is proportional to theamplitude of a corresponding instantaneous portion of an expectedreflection of a seismic wave.

4. The new use, for analysis of a seismic waveform varying with time, ofan apparatus comprising a tapped delay line providing simultaneously aplurality of outputs each of which represents the value of a waveform ata predetermined different instant of time, means receiving said outputsand multiplying each by a predetermined individual constant to provideproduct outputs, means receiving said product outputs and summing themto provide a summed output, and means for recording said summed outputas a function of the time scale of said waveform, said new use involvingintroducing a seismic waveform to the apparatus as the waveform involvedand adjusting the apparatus to provide as each individual constant theamplitude of a corresponding instantaneous portion of an expectedreflection of a seismic wave.

5. The new use, for analysis of a seismic waveform varying with time, ofan apparatus comprising a tapped delay line providing simultaneously aplurality of outputs each of which represents the value of a waveform ata predetermined different instant of time, means comprising a pluralityof attenuators individual to said outputs receiving said outputs andmultiplying each by a predetermined individual constant to provideproduct outputs, means receiving said product outputs and summing themto provide a summed output and means for recording said summed output asa function of the time scale of said waveform, said new use involvingintroducing a seismic waveform to the apparatus as the Waveform involvedand adjusting said attenuators to provide as each of said individualconstants the amplitude of a corresponding instantaneous portion of anexpected reflection of a seismic wave.

References Cited by the Examiner UNITED STATES PATENTS 2,179,000 11/1939Tea 8814 2,243,730 5/1941 Ellis.

2,643,819 6/1953 Lee et a1 235-181 2,676,206 4/1954 Bennett et a1235-181 X 2,794,965 6/1957 Yost 34015 2,801,351 7/1957 Calvert et a1307-149 2,839,149 6/1958 Piety.

2,885,590 5/1959 Fuller 235-l81 X MALCOLM A. MORRISON, Primary Examiner.

ABRAHAM BERLIN, LEO SMILOW, CORNELIUS D.

ANGEL, Examiners.

1. THE NEW USE, FOR ANALYSIS OF A SEISMIC WAVEFORM VARYING WITH TIME, OFAN APPARATUS WHICH PROVIDES AT ANY INSTANT AN OUTPUT COMPRISING PRODUCTSOF CORRESPONDING VALUES OF A WAVEFORM AND OF A PREDETERMINED WAVELET,MEANS SUMMING SAID PRODUCTS OVER A PREDETERMINED TIME PERIOD OF THEWAVEFORM, SAID SUMMATION BEING CONTINUOUSLY CARRIED OUT TO PROVIDE ACONTINUOUS INTEGRAL OUTPUT, AND MEANS RECORDING SAID INTEGRAL OUTPUT ASA FUNCTION OF THE TIME SCALE OF SAID WAVEFORM, SAID NEW USE INVOLVINGINTRODUCING A SEISMIC WAVEFORM TO THE APPARATUS AS THE WAVEFORM INVOLVEDAND ADJUSTING THE APPARATUS TO PROVIDE AS THE WAVELET ONE HAVING THEFORM OF AN EXPECTED REFLECTION OF A SEISMIC WAVE.